IRIX Base Documentation 2001 May/SGI IRIX Base Documentation 2001 May.iso/usr/share/catman/p_man/cat3/perl5/Math::Trig.z/Math::Trig

Text File | 1998-10-30 | 7.4 KB | 265 lines

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     Math::Trig - trigonometric functions

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             use Math::Trig;

             $x = tan(0.9);
             $y = acos(3.7);
             $z = asin(2.4);

             $halfpi = pi/2;

             $rad = deg2rad(120);


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     Math::Trig defines many trigonometric functions not defined by the core
     Perl which defines only the sin() and cos().  The constant ppppiiii is also
     defined as are a few convenience functions for angle conversions.

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     The tangent

             tan

     The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cot
     are aliases)

             csc cosec sec cot cotan

     The arcus (also known as the inverse) functions of the sine, cosine, and
     tangent

             asin acos atan

     The principal value of the arc tangent of y/x

             atan2(y, x)

     The arcus cofunctions of the sine, cosine, and tangent (acosec/acsc and
     acotan/acot are aliases)

             acsc acosec asec acot acotan

     The hyperbolic sine, cosine, and tangent

             sinh cosh tanh

     The cofunctions of the hyperbolic sine, cosine, and tangent (cosech/csch
     and cotanh/coth are aliases)





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             csch cosech sech coth cotanh

     The arcus (also known as the inverse) functions of the hyperbolic sine,
     cosine, and tangent

             asinh acosh atanh

     The arcus cofunctions of the hyperbolic sine, cosine, and tangent
     (acsch/acosech and acoth/acotanh are aliases)

             acsch acosech asech acoth acotanh

     The trigonometric constant ppppiiii is also defined.

             $pi2 = 2 * pi;


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     The following functions

             tan
             sec
             csc
             cot
             asec
             acsc
             tanh
             sech
             csch
             coth
             atanh
             asech
             acsch
             acoth

     cannot be computed for all arguments because that would mean dividing by
     zero or taking logarithm of zero. These situations cause fatal runtime
     errors looking like this

             cot(0): Division by zero.
             (Because in the definition of cot(0), the divisor sin(0) is 0)
             Died at ...

     or

             atanh(-1): Logarithm of zero.
             Died at...

     For the csc, cot, asec, acsc, acot, csch, coth, asech, acsch, the
     argument cannot be 0 (zero).  For the atanh, acoth, the argument cannot
     be 1 (one).  For the atanh, acoth, the argument cannot be -1 (minus one).



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     For the tan, sec, tanh, sech, the argument cannot be _p_i/_2 + _k * _p_i, where
     _k is any integer.

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     Please note that some of the trigonometric functions can break out from
     the rrrreeeeaaaallll aaaaxxxxiiiissss into the ccccoooommmmpppplllleeeexxxx ppppllllaaaannnneeee. For example asin(2) has no
     definition for plain real numbers but it has definition for complex
     numbers.

     In Perl terms this means that supplying the usual Perl numbers (also
     known as scalars, please see the _p_e_r_l_d_a_t_a manpage) as input for the
     trigonometric functions might produce as output results that no more are
     simple real numbers: instead they are complex numbers.

     The Math::Trig handles this by using the Math::Complex package which
     knows how to handle complex numbers, please see the _M_a_t_h::_C_o_m_p_l_e_x manpage
     for more information. In practice you need not to worry about getting
     complex numbers as results because the Math::Complex takes care of
     details like for example how to display complex numbers. For example:

             print asin(2), "\n";

     should produce something like this (take or leave few last decimals):

             1.5707963267949-1.31695789692482i

     That is, a complex number with the real part of approximately 1.571 and
     the imaginary part of approximately -1.317.

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     (Plane, 2-dimensional) angles may be converted with the following
     functions.

             $radians  = deg2rad($degrees);
             $radians  = grad2rad($gradians);

             $degrees  = rad2deg($radians);
             $degrees  = grad2deg($gradians);

             $gradians = deg2grad($degrees);
             $gradians = rad2grad($radians);

     The full circle is 2 _p_i radians or _3_6_0 degrees or _4_0_0 gradians.

BBBBUUUUGGGGSSSS
     Saying use Math::Trig; exports many mathematical routines in the caller
     environment and even overrides some (sin, cos).  This is construed as a
     feature by the Authors, actually... ;-)






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     The code is not optimized for speed, especially because we use
     Math::Complex and thus go quite near complex numbers while doing the
     computations even when the arguments are not. This, however, cannot be
     completely avoided if we want things like asin(2) to give an answer
     instead of giving a fatal runtime error.

AAAAUUUUTTTTHHHHOOOORRRRSSSS
     Jarkko Hietaniemi <_j_h_i@_i_k_i._f_i> and Raphael Manfredi
     <_R_a_p_h_a_e_l__M_a_n_f_r_e_d_i@_g_r_e_n_o_b_l_e._h_p._c_o_m>.














































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